Expansion of a quantum electron gas

The dynamics of a quantum plasma can be described self-consistently by the nonlinear Schrödinger-Poisson system. Here, we consider a multistream model representing a statistical mixture of N pure states, each described by a wavefunction. The one-stream and two-stream cases are investigated. We derive the dispersion relation for the two-stream instability and show that a new, purely quantum, branch appears. Numerical simulations of the complete Schrödinger-Poisson system confirm the linear analysis, and provide further results in the strongly nonlinear regime. The stationary states of the Schrödinger-Poisson system are also investigated. These can be viewed as the quantum mechanical counterpart of the classical Bernstein-Greene-Kruskal modes, and are described by a set of coupled nonlinear differential equations for the electrostatic potential and the stream amplitudes.

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“…If all quantities are dependent only on position, Eqs. (5)- (6) for N = 2 possess the first integrals…”

Section: Stationary Solutions -Qbgk Modesmentioning

confidence: 99%

Multistream model for quantum plasmas

Haas¹,

Manfredi²,

2000

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“…By introducing an appropriate time-dependent scaling of the spatial coordinates, they were able to transform the problem to a free-particle motion and to derive an exact analytical solution. Later on, Manfredi et al [16,17] introduced a time-dependent scaling of both space and time variables to freeze the expansion into a vacuum of both a one-dimensional, collisionless, two-species classical plasma and a quantum electron gas in planar geometry. In atomic and molecular physics, Solov'ev and Vinitsky [18] and later on, Ovchinnikov et al [19] treated the Coulomb three-body problem, in particular ion-atom and atom-atom collisions, within a proper adiabatic representation by timescaling the internuclear distance.…”

Section: Introductionmentioning

confidence: 99%

Time scaling with efficient time-propagation techniques for atoms and molecules in pulsed radiation fields

et al. 2011

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We present an ab initio approach to solving the time-dependent Schrödinger equation to treat electron-and photon-impact multiple ionization of atoms or molecules. It combines the already known time-scaled coordinate method with a high-order time propagator based on a predictor-corrector scheme. In order to exploit in an optimal way the main advantage of the time-scaled coordinate method, namely, that the scaled wave packet stays confined and evolves smoothly toward a stationary state, of which the squared modulus is directly proportional to the electron energy spectra in each ionization channel, we show that the scaled bound states should be subtracted from the total scaled wave packet. In addition, our detailed investigations suggest that multiresolution techniques like, for instance, wavelets are the most appropriate ones to represent the scaled wave packet spatially. The approach is illustrated in the case of the interaction of a one-dimensional model atom as well as atomic hydrogen with a strong oscillating field.

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“…For quantum plasmas, recent applications include quantum plasma echoes, 8 the expansion of a quantum electron gas into vacuum, 9 quantum plasma instabilities, 10 the self-consistent dynamics of Fermi gases, 11 and quantum Penrose diagrams. For quantum plasmas, recent applications include quantum plasma echoes, 8 the expansion of a quantum electron gas into vacuum, 9 quantum plasma instabilities, 10 the self-consistent dynamics of Fermi gases, 11 and quantum Penrose diagrams.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear quantum dust acoustic waves in nonuniform complex quantum dusty plasma

2007

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The quantum hydrodynamic model for plasmas is employed to study the dynamics of the nonlinear quantum dust acoustic ͑QDA͒ wave in a nonuniform quantum dusty plasma ͑QDP͒. Through the reductive perturbation technique, it is shown that the quantum hydrodynamical basic equations describing the nonlinear QDA waves yield a modified Korteweg-de Veries equation with slowly varying coefficients in the system inhomogeneity. Applying generalized expansion method, it is found that the system admits only rarefactive solitons. The properties of the solitons such as the velocity, the amplitude and the width of the nonlinear QDA waves are analyzed using appropriate choice for initial ion and electron density numbers. For the homogeneous QDP, no critical value is found. Because of the system inhomogeneity, a new criticality is found forcing with the usage of new stretching coordinates. A higher evolution equation with third-order nonlinearity is derived at the critical values. The solution of the latter equation admits rarefactive shock wave attached with an amplitude factor. The present investigations should be useful for researches on astrophysical plasmas as well as for ultra small micro-and nano-electronic devices.

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Expansion of a quantum electron gas

Cited by 61 publications

References 15 publications

Multistream model for quantum plasmas

Multistream model for quantum plasmas

Time scaling with efficient time-propagation techniques for atoms and molecules in pulsed radiation fields

Nonlinear quantum dust acoustic waves in nonuniform complex quantum dusty plasma

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